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   "source": [
    "# The stereology module\n",
    "\n",
    "The main purpose of stereology is to extract quantitative information from microscope images relating two-dimensional measures obtained on sections to three-dimensional parameters defining the structure. The aim of stereology is not to reconstruct the 3D geometry of the material (as in tomography) but to estimate  a particular 3D feature. In this case, we aim to approximate the actual (3D) grain size distribution from the apparent (2D) grain size distribution obtained in sections.\n",
    "\n",
    "GrainSizeTools script includes two stereological methods: 1) the Saltykov, and 2) the two-step methods. Before looking at its functionalities, applications and limitations, let's import the example dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "module plot imported\nmodule averages imported\nmodule stereology imported\nmodule piezometers imported\nmodule template imported\n\n======================================================================================\nWelcome to GrainSizeTools script\n======================================================================================\nA free open-source cross-platform script to visualize and characterize grain size\npopulation and estimate differential stress via paleopizometers.\n\nVersion: v3.0.2 (2020-12-30)\nDocumentation: https://marcoalopez.github.io/GrainSizeTools/\n\nType get.functions_list() to get a list of the main methods\n\n"
     ]
    }
   ],
   "source": [
    "# Load the script first (change the path to GrainSizeTools_script.py accordingly!)\n",
    "%run C:/Users/marco/Documents/GitHub/GrainSizeTools/grain_size_tools/GrainSizeTools_script.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import the example dataset\n",
    "filepath = 'C:/Users/marco/Documents/GitHub/GrainSizeTools/grain_size_tools/DATA/data_set.txt'\n",
    "dataset = pd.read_csv(filepath, sep='\\t')\n",
    "dataset['diameters'] = 2 * np.sqrt(dataset['Area'] / np.pi)  # estimate ECD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Saltykov method\n",
    "\n",
    "> **What is it?**\n",
    ">\n",
    "> It is a stereological method that approximates the actual grain size distribution from the histogram of the apparent grain size distribution. The method is distribution-free, meaning that no assumption is made upon the type of statistical distribution, making the method very versatile.\n",
    ">\n",
    "> **What do I use it for?**\n",
    ">\n",
    "> Its main use (in geosciences) is to estimate the volume fraction of a specific range of grain sizes.\n",
    ">\n",
    "> **What are its limitations?**\n",
    ">\n",
    "> The method presents several limitations for its use in rocks\n",
    ">\n",
    "> - It assumes that grains are non-touching spheres uniformly distributed in a matrix (e.g. bubbles within a piece of glass). This never holds for polycrystalline rocks. To apply the method, the grains should be at least approximately equiaxed, which is normally fulfilled in recrystallized grains.\n",
    "> - Due to the use of the histogram, the number of classes determines the accuracy and success of the method. There is a trade-off here because the smaller the number of classes, the better the numerical stability of the method, but the worse the approximation of the targeted distribution and vice versa. The issue is that no method exists to find an optimal number of classes and this has to be set by the user. The use of the histogram also implies that we cannot obtain a complete description of the grain size distribution.\n",
    "> - The method lacks a formulation for estimating errors during the unfolding procedure.\n",
    "> - You cannot obtain an estimate of the actual average grain size (3D) as individual data is lost when using the histogram (i.e. The Saltykov method reconstructs the 3D histogram, not every apparent diameter in the actual one as this is mathematically impossible).\n",
    ">\n",
    "\n",
    "TODO: explain the details of the method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "=======================================\nvolume fraction (up to 50 microns) = 41.65 %\n=======================================\n=======================================\nbin size = 14.24\n=======================================\n"
     ]
    },
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "fig1, (ax1, ax2) = stereology.Saltykov(dataset['diameters'], numbins=11, calc_vol=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig1.savefig(\"saltykov_plot.png\", dpi=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's assume that we want to use the class densities estimated by Saltykov's method to calculate the specific volume of each or one of the classes. We have two options here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "\u001b[1;31mSignature:\u001b[0m\n",
      "\u001b[0mstereology\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mSaltykov\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mdiameters\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mnumbins\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mcalc_vol\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mtext_file\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mreturn_data\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m    \u001b[0mleft_edge\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n",
      "\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mDocstring:\u001b[0m\n",
      "Estimate the actual (3D) distribution of grain size from the population\n",
      "of apparent diameters measured in a thin section using a Saltykov-type\n",
      "algorithm (Saltykov 1967; Sahagian and Proussevitch 1998).\n",
      "\n",
      "The Saltykov method is optimal to estimate the volume of a particular grain\n",
      "size fraction as well as to obtain a qualitative view of the appearance of\n",
      "the actual 3D grain size population, either in uni- or multimodal populations.\n",
      "\n",
      "Parameters\n",
      "----------\n",
      "diameters : array_like\n",
      "    the apparent diameters of the grains.\n",
      "\n",
      "numbins : positive integer, optional\n",
      "    the number of bins/classes of the histogram. If not declared,\n",
      "    is set to 10 by default.\n",
      "\n",
      "calc_vol : positive scalar or None, optional\n",
      "    if the user specifies a diameter, the function will return the volume\n",
      "    occupied by the grain fraction up to that diameter.\n",
      "\n",
      "text_file : string or None, optional\n",
      "    if the user specifies a name, the function will store a csv file\n",
      "    with that name containing the Saltykov output.\n",
      "\n",
      "return_data : bool, optional\n",
      "   if True the function will return the position of the midpoints and\n",
      "   the frequencies.\n",
      "\n",
      "left_edge : positive scalar or 'min', optional\n",
      "    set the left edge of the histogram. Default is zero.\n",
      "\n",
      "Call functions\n",
      "--------------\n",
      "- unfold_population\n",
      "- Saltykov_plot\n",
      "\n",
      "Examples\n",
      "--------\n",
      ">>> Saltykov(diameters)\n",
      ">>> Saltykov(diameters, numbins=16, calc_vol=40)\n",
      ">>> Saltykov(diameters, text_file='foo.csv')\n",
      ">>> mid_points, frequencies = Saltykov(diameters, return_data=True)\n",
      "\n",
      "References\n",
      "----------\n",
      "Saltykov SA (1967) http://doi.org/10.1007/978-3-642-88260-9_31\n",
      "Sahagian and Proussevitch (1998) https://doi.org/10.1016/S0377-0273(98)00043-2\n",
      "\n",
      "Return\n",
      "------\n",
      "Statistical descriptors, a plot, and/or a file with the data (optional)\n",
      "\u001b[1;31mFile:\u001b[0m      c:\\users\\marco\\documents\\github\\grainsizetools\\grain_size_tools\\stereology.py\n",
      "\u001b[1;31mType:\u001b[0m      function\n"
     ],
     "name": "stdout"
    }
   ],
   "source": [
    "stereology.Saltykov?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input parameter ``text_file`` allows you to save a text file with the data in tabular format, you only have to declare the name of the file and the file type, either txt or csv (as in the function documentation example). Alternatively, you can use the Saltykov function to directly return the density and the midpoint values of the classes as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[1.31536871e-03 2.17302235e-02 2.25631643e-02 1.45570771e-02\n 6.13586532e-03 2.24830266e-03 1.29306084e-03 3.60326809e-04\n 0.00000000e+00 0.00000000e+00 4.11071036e-05]\n"
     ]
    }
   ],
   "source": [
    "mid_points, densities = stereology.Saltykov(dataset['diameters'], numbins=11, return_data=True)\n",
    "print(densities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you may notice, these density values do not add up to 1 or 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0.07024449636922886"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "source": [
    "np.sum(densities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is because the script normalized the frequencies of the different classes so that the integral over the range (not the sum) is one (see FAQs for an explanation on this). If you want to calculate the relative proportion for each class you must multiply the value of the densities by the bin size. After doing this, you can check that the relative densities sum one (i.e. they are proportions relative to one)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "1.000000650312342"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "corrected_densities = densities * 14.236\n",
    "np.sum(corrected_densities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So for example if you have a volume of rock of say 100 cm2 and you want to estimate what proportion of that volume is occupied by each grain size class/range, you could estimate it as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ 1.87, 30.94, 32.12, 20.72,  8.74,  3.2 ,  1.84,  0.51,  0.  ,\n",
       "        0.  ,  0.06])"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "# I use np.around to round the values\n",
    "np.around(corrected_densities * 100, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The two-step method\n",
    "\n",
    "> **What is it?**\n",
    ">\n",
    "> It is a stereological method that approximates the actual grain size distribution. The method is distribution-dependent, meaning that it is assumed that the distribution of grain sizes follows a lognormal distribution. The method fit a lognormal distribution on top of the Saltykov output, hence the name two-step method.\n",
    ">\n",
    "> **What do I use it for?**\n",
    ">\n",
    "> Its main use is to estimate the shape of the lognormal distribution, the average grain size (3D), and the volume fraction of a specific range of grain sizes (not yet implemented).\n",
    ">\n",
    "> **What are its limitations?**\n",
    ">\n",
    ">  The method is partially based on the Saltykov method and therefore inherits some of its limitations. The method however do not require to define a specific number of classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "=======================================\nPREDICTED OPTIMAL VALUES\nNumber of classes: 11\nMSD (lognormal shape) = 1.63 ± 0.06\nGeometric mean (scale) = 36.05 ± 1.27\n=======================================\n"
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\n"
     },
     "metadata": {}
    }
   ],
   "source": [
    "fig2, ax = stereology.calc_shape(dataset['diameters'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig2.savefig(\"2step_plot.png\", dpi=150)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}